In this article, we introduce trigmm , a package designed to estimate the parameters of triangular two-equation systems without the need for instrumental variables. The trigmm command leverages the identification conditions proposed by Lewbel, Schennach, and Zhang (2024, Journal of Business and Economic Statistics 42: 14–25), enabling instrument-free identification primarily through the non-Gaussianity assumption of error variables. We also introduce the trigmmset command, which provides bounds on the parameters based on the set identification results from the same article even without the non-Gaussianity assumption, offering complementary analyses alongside the trigmm command. Estimation is performed by integrating these moment conditions with Stata’s built-in generalized method of moments ( gmm ) framework. The package’s functionality is demonstrated through an empirical application.
Brown et al. (Sun,) studied this question.